Respuesta :
Answer:
the mass of the cart is 150 kg
Explanation:
given,
mass of boy(m) = 50 kg
speed of boy (v)= 10 m/s
initial velocity of cart (u) = 0
final velocity of cart(V) = 2.5 m/s
mass of the cart(M) = ?
m v + M u = (m + M ) V......................(1)
50× 10 + 0 = (50 + M ) 2.5
M =[tex]\dfrac{500}{2.5} - 50[/tex]
M = 150 Kg
hence, the mass of the cart is 150 kg
Answer:
Mass of the cart is 750 kg
Given:
Mass of the boy, m = 50 kg
Speed of the boy, v = 10.0 m/s
Final speed of the boy with the cart, v' = 2.5 m/s
Solution:
Initially the cart is at rest and since its on the ground, height, h = 0
Now, by the conservation of energy, mechanical energy before and after will remain conserved:
KE + PE = KE' + PE' (1)
where
KE = Initial Kinetic energy
KE' = Final Kinetic Energy
PE = Initial Potential Energy
PE' = Final Potential Energy
We know that:
Kinetic enrgy = [tex]\frac{1}{2}mv^{2}[/tex]
Potential energy = mgh
Since, potential energy will remain zero, thus we apply the conservation of Kinetic Energy only.
Let the mass of cart be M, thus the mass of the system, m' = 50 + M
Using eqn (1):
[tex]\frac{1}{2}mv^{2} = \frac{1}{2}m'v^{2}[/tex]
[tex]\frac{1}{2}\times 50\times 10^{2} = \frac{1}{2}(50 + M)\times 2.5^{2}[/tex]
[tex]5000 = 6.25(50 + M)[/tex]
M = 750 kg
