Question

a trolley of mass 200 kg carrying a sandbag of mass 20 kg is moving on a frictionless horizontal track with speed 36 kh/hr. after a while, sand starts leaking out of the bag on the floor of trolley at the rate 0.04 kg/sec. what is the speed of trolley after the entire sand bag is empty?

Answer 1

The speed of the trolley after the entire sandbag is empty is 39 km/hr.

Step-by-step explanation:

Initially, the momentum of the system is conserved. The momentum (p) is given by the product of mass (m) and velocity (v), i.e., p = m * v. The total initial momentum of the system is the sum of the trolley and sandbag momenta. As sand leaks, there is no external horizontal force acting on the system, so the horizontal component of the total momentum remains constant.

The initial momentum (p_initial) is the sum of the trolley and sandbag momenta:

`\[ p_{\text{initial}} = (m_{\text{trolley}} + m_{\text{sandbag}}) \cdot v_{\text{initial}} \]`

As the sand leaks, the mass of the sandbag decreases with time. The final momentum (p_final) is the momentum of the trolley when the sandbag is empty:

`\[ p_{\text{final}} = m_{\text{trolley}} \cdot v_{\text{final}} \]`

Since momentum is conserved,
`\( p_{\text{initial}} = p_{\text{final}} \):\[ (m_{\text{trolley}} + m_{\text{sandbag}}) \cdot v_{\text{initial}} = m_{\text{trolley}} \cdot v_{\text{final}} \]`

We can then solve for the final velocity
`(\( v_{\text{final}} \))`:

`\[ v_{\text{final}} = \frac{m_{\text{trolley}} + m_{\text{sandbag}}}{m_{\text{trolley}}} \cdot v_{\text{initial}} \]`

Substituting the given values, we get:

`\[ v_{\text{final}} = (200 + 20)/(200) \cdot 36 \, \text{km/hr} = 39 \, \text{km/hr} \]`