Name: Motion With Variable Acceleration
Uploaded: 2019-07-19
Duration: 10 min 54 s
Description: You may be aware of the SUVAT equation, but do you think this can be applicable for all types of motion? No, what are those motion? Watch this to find out.

Question

A mass $m$ of $4.0 kg$ slides down a frictionless incline of $θ = 30^{°}$ to the horizontal. The mass starts from rest from a height of $20 m$ .

Sketch a graph of the kinetic and potential energies of the mass as a function of time.

Accepted Answer

The given situation is shown from the following diagram

From the figure initial potential energy is

$P . E_{i} = m g h = 4 \times 9.8 \times 20 = 785 J$

Now the potential energy at any point during the motion can be written as follows

$P . E = P . E_{i} - m g y$

Here $y$ is the vertical distance travelled by the mass.

From the figure $y = s \times \sin (30 °)$

According to the equation of motion $s = u t + \frac{1}{2} a t^{2}$

$u = 0$ , Since the mass started from rest, the acceleration in the direction of displacement is $g \sin (30 °)$

Hence, $s = \frac{1}{2} \times g \sin (30 °) \times t^{2} = \frac{1}{2} \times 9.8 \times \frac{1}{2} \times t^{2} = 2.45 t^{2}$

So, $y = 2.45 t^{2} \times \sin (30 °) = 2.45 t^{2} \times \frac{1}{2} = 1.23 t^{2}$

Substitute $y$ in potential energy $P . E = 785 - 4 \times 9.8 \times 1.23 t^{2}$

$P . E = 785 - 48 t^{2}$

Since the surface is frictionless total energy is conserved.

$K . E_{i} + P . E_{i} = K . E_{y} + P . E_{y}$

$K . E_{y} = P . E_{i} + K . E_{i} - P . E_{y}$

Initially, velocity is zero, $K . E_{i} = 0$

By putting all values in the above equation

$K . E_{y} = 785 + 0 - (785 - 48 t^{2}) = 48 t^{2}$

So the graph of the potential and kinetic energies as a function of time are shown below $:$

A mass $m$ of $4.0 kg$ slides down a frictionless incline of $θ = 30^{°}$ to the horizontal. The mass starts from rest from a height of $20 m$ .

Sketch a graph of the kinetic and potential energies of the mass as a function of time.

Important Questions on Mechanics

Learn and Prepare for any exam you want !

A mass m of 4.0 kg slides down a frictionless incline of θ=30° to the horizontal. The mass starts from rest from a height of 20 m. Sketch a graph of the kinetic and potential energies of the mass as a function of time.

Important Questions on Mechanics

Learn and Prepare for any exam you want !

A mass $m$ of $4.0 kg$ slides down a frictionless incline of $θ = 30^{°}$ to the horizontal. The mass starts from rest from a height of $20 m$ .

Sketch a graph of the kinetic and potential energies of the mass as a function of time.