Question

A block is released from rest, at a height h, and allowed to slide down an inclined plane. There is friction on the plane. At the bottom of the plane, there is a spring that the block will compress. After compressing the spring, the block will slide up the plane to some maximum height, hA, after which it will again slide back down. How much work is done on the block between its release at height h and its ascent to its next maximum height?
1. More information is needed.
2. 2µ mA g hA
3. mA g (h − hA)
4. 0
5. mA g (h − hA) + 2µ mA g hA
6. None of these

Answer 1

Here the block has two work done on it

1. Work done by gravity

2. Work done by friction force

So here it start from height "h" and then again raise to height hA after compressing the spring

So work done by the gravity is given as

$W_g = m_A g(h - h_A)$

Now work done by the friction force is to be calculated by finding total path length because friction force is a non conservative force and its work depends on total path

$W_f = -(\mu m_A g cos\theta)(\frac{h}{sin\theta} + \frac{h_A}{sin\theta})$

$W_f = -\mu m_A g cot\theta(h + h_A)$

Total work done on it

$W = m_A g(h - h_A) - \mu m_A g cot\theta(h + h_A)$

So answer will be

None of these

Answer 2

The work done on the block between its release from height $h$ and its ascent to the height ${h_A}$ will be $\boxed0$.

Further Explanation:

The block is released from a particular height from rest. It means that the block has only the potential energy stored in it. The kinetic energy of the block is zero.

Now as the block comes to the bottom of the plane on the rough incline and compresses the spring, it losses some of the energy and some energy is stored in the spring as spring potential energy.

The spring finally rebounds to some height ${h_A}$ where the block finally comes to rest and then starts to slide back.

During its motion from the starting point to the height ${h_A}$, the kinetic energy of the block remains same at the initial and final position because initially it was at rest and finally at ${h_A}$ it is again at rest.

According to the work energy theorem, the amount of work done on the system is equal to the change in the kinetic energy of the system. Here, the change in kinetic energy of the system is zero. So, the work done on the system will also be zero.

Thus, the work done on the block between its release from height $h$ and its ascent to the height ${h_A}$ will be $\boxed0$.

Learn More:

1. In the calorimetry experiment which energy will be calculated during the heat exchange if water is used brainly.com/question/2566525

2. To what volume will a 2.33 l sample of gas expand if it is heated from 30.0 c to 300.0 c brainly.com/question/9979757

3. One consequence of the third law of thermodynamics is that brainly.com/question/3564634

Answer Details:

Grade: Senior School

Subject: Physics

Chapter: Work-Energy Theorem

Keywords:  Block released from rest, down an inclined plane, compress, a spring, work energy theorem, change in kinetic energy, maximum height.