Two horizontal forces F → 1 and F → 2 act on a 4 . 0 kg disk that slides over frictionless ice, on which an x, y coordinate system is laid out. Force F → 1 is in the positive direction of the x axis and has a magnitude of 7 . 0 N . Force F → 2 has a magnitude of 9 . 0 N . The figure shown below gives the x component v x of the velocity of the disk as a function of time t during the sliding. What is the angle between the constant directions of forces F → 1 and F → 2 ?

Here the slope of the line gives the acceleration along X direction a x = Slope of v x - t from graph. From the given diagram a x = 5 - 2 3 - 2 = 3 m s - 2 Let F x is the magnitude of the resultant force along x -axis F x = m a x = 4 ( 3 ) = 12 N Where m = mass of the object Given that F 1 is along X direction and has a magnitude of 7 N F 2 has a magnitude of 9 N and has a component F 2 c o s θ along x axis Hence, net force along x axis is given as F x = F 1 + F 2 c o s θ Where θ is the angle between F 1 → and F 2 → Now finding angle between them c o s θ = F x - F 1 F 2 = 12 - 7 9 = 0 . 555 θ = c o s - 1 0 . 555 = 56 . 3 °

Two horizontal forces F → 1 and F → 2 act on a 4 . 0 kg disk that slides over frictionless ice, on which an x, y coordinate system is laid out. Force F → 1 is in the positive direction of the x axis and has a magnitude of 7 . 0 N . Force F → 2 has a magnitude of 9 . 0 N . The figure shown below gives the x component v x of the velocity of the disk as a function of time t during the sliding. What is the angle between the constant directions of forces F → 1 and F → 2 ?

Here the slope of the line gives the acceleration along X direction a x = Slope of v x - t from graph. From the given diagram a x = 5 - 2 3 - 2 = 3 m s - 2 Let F x is the magnitude of the resultant force along x -axis F x = m a x = 4 ( 3 ) = 12 N Where m = mass of the object Given that F 1 is along X direction and has a magnitude of 7 N F 2 has a magnitude of 9 N and has a component F 2 c o s θ along x axis Hence, net force along x axis is given as F x = F 1 + F 2 c o s θ Where θ is the angle between F 1 → and F 2 → Now finding angle between them c o s θ = F x - F 1 F 2 = 12 - 7 9 = 0 . 555 θ = c o s - 1 0 . 555 = 56 . 3 °

A 550 kg rocket sled can be accelerated at a constant rate from rest to 1650 km h - 1 in 2 . 0 s . What is the magnitude of the required net force?

Given, mass of the rocket m = 550 kg . It starts from rest. Its initial velocity, u = 0 . Final velocity v = 1650 km h - 1 = 1650 × 5 18 m s - 1 = 458 . 3 m s - 1 . Time needed for the velocity to get changed, t = 2 s . As acceleration can change the velocity of the rocket, using the equation of motion, we can calculate the acceleration a , v - u = a t . . . ( 1 ) Substitute given values in equation ( 1 ) , ⇒ a = v - u t = 458 . 3 - 0 2 ⇒ a = 229 . 15 m s - 2 Using Newton's second law of motion, the net force on the rocket, F → = m a → . . . ( 2 ) . Substitute given values in equation ( 2 ) , ⇒ F → = 550 × 229 . 15 = 126032 . 5 N ⇒ F → ≃ 126 kN .

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Two horizontal forces ${\vec{F}}_{1}$ and ${\vec{F}}_{2}$ act on a $4.0 kg$ disk that slides over frictionless ice, on which an x, y coordinate system is laid out. Force ${\vec{F}}_{1}$ is in the positive direction of the x axis and has a magnitude of $7.0 N$ . Force ${\vec{F}}_{2}$ has a magnitude of $9.0 N$ . The figure shown below gives the x component $v_{x}$ of the velocity of the disk as a function of time t during the sliding. What is the angle between the constant directions of forces ${\vec{F}}_{1}$ and ${\vec{F}}_{2} ?$

Important Questions on Force and Motion-I

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Principles Of Physics International Student Version>Chapter 5 - Force and Motion-I>Problems>Q 13

Two particles of masses $m$ and $2 m$ are placed on a smooth horizontal table. A string, which joins these two masses, hangs over the edge supporting a pulley, which suspends a particle of mass $3 m$ , in figure shown below. The pulley has negligible mass. The two parts of the string on the table are parallel and perpendicular to the edge of the table. The hanging parts of the string are vertical. Find the acceleration of the particle of mass $3 m$ .

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Principles Of Physics International Student Version>Chapter 5 - Force and Motion-I>Problems>Q 14

A block with a weight of

4.0 N

is at rest on a horizontal surface. A

1.0 N

upward force is applied to the block by means of an attached vertical string. What are the magnitude and the direction of the force of the block on the horizontal surface?

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Principles Of Physics International Student Version>Chapter 5 - Force and Motion-I>Problems>Q 15

$(a)$ A $11.0 kg$ salami is supported by a cord that runs to a spring scale, which is supported by a cord, hanging from the ceiling in the figure shown below. What is the reading on the scale, which is marked in the SI weight units? (This is a way to measure the weight by a deli owner.)
$(b)$ In the figure shown below, the salami is supported by a cord that runs around a pulley and to a scale. The opposite end of the scale is attached by a cord to a wall. What is the reading on the scale? (This is the way by a physics major.)
$(c)$ In the figure shown below, the wall has been replaced with a second $11.0 kg$ salami, and the assembly is stationary. What is the reading on the scale? (This is the way by a deli owner who was once a physics major.)

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Principles Of Physics International Student Version>Chapter 5 - Force and Motion-I>Problems>Q 16

Some insects can walk below a thin rod (such as a twig) by hanging from it. Suppose that, such an insect has mass $m$ and hangs from a horizontal rod, as shown in the figure shown below, with angle $θ = 40 °$ . Its six legs are all under the same tension, and the leg sections nearest the body are horizontal.

(a) What is the ratio of the tension in each tibia (forepart of a leg) to the insect's weight?

(b) If the insect straightens out its legs somewhat, does the tension in each tibia increase, decrease, or stay the same?

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Principles Of Physics International Student Version>Chapter 5 - Force and Motion-I>Problems>Q 17

In the figure shown below, let the mass of the block be $8.5 kg$ and angle $θ$ be $30 °$ . Find

(a) the tension in the cord.

(b) the normal force acting on the block.

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Principles Of Physics International Student Version>Chapter 5 - Force and Motion-I>Problems>Q 18

In April 1974, John Massis of Belgium managed to move two passenger railroad cars. He did so by clamping his teeth down on a bit that was attached to the cars with a rope and then leaning backwards while pressing his feet against the railway ties. The cars together weighed

700 kN

(about

80 tons

). Assume that, he pulled with a constant force that was

2.5

times his body weight, at an upward angle

θ

30 °

from the horizontal. His mass was

80 kg

, and he moved the cars by

1.0 m

. Neglecting any retarding force from the wheel rotation, find the speed of the cars at the end of the pull.

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Principles Of Physics International Student Version>Chapter 5 - Force and Motion-I>Problems>Q 19

550 kg

rocket sled can be accelerated at a constant rate from rest to

1650 km h^{- 1}

2.0 s

. What is the magnitude of the required net force?

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IMPORTANT

Principles Of Physics International Student Version>Chapter 5 - Force and Motion-I>Problems>Q 20

A car travelling at

63 km h^{- 1}

hits a bridge abutment. A passenger in the car moves forward a distance of

65 cm

(with respect to the road) while being brought to rest by an inflated airbag. What magnitude of force (assumed constant) acts on the passenger's upper torso, which has a mass of

41 kg ?

Important Questions on Force and Motion-I

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