Question
A 50.0-kg boy runs on a horizontal surface at a speed of 10.0 m/s
and jumps onto a cart just before reaching a slope as shown in the figure. The cart is initially
at rest. If the mass of the cart is 150 kg, what is the maximum height h the boy/cart will reach
up the slope assuming the slope has no friction?
and jumps onto a cart just before reaching a slope as shown in the figure. The cart is initially
at rest. If the mass of the cart is 150 kg, what is the maximum height h the boy/cart will reach
up the slope assuming the slope has no friction?
Answers
We don't see the diagram, but assume that the cart is at the beginning of an uphill slope of angle θ with the horizontal.
The problem comes to a matter of conservation of energy, since friction is neglected.
Kinetic energy of the running boy
KE= (1/2) mv²=(1/2)50(10^2)=2500 J.
Assume the height reached is h, then
potential energy is
PE=mgh=50*9.81*h
Since energy is (assumed) conserved, we have KE=PE
50(9.81)h=2500
Solve for h.
The problem comes to a matter of conservation of energy, since friction is neglected.
Kinetic energy of the running boy
KE= (1/2) mv²=(1/2)50(10^2)=2500 J.
Assume the height reached is h, then
potential energy is
PE=mgh=50*9.81*h
Since energy is (assumed) conserved, we have KE=PE
50(9.81)h=2500
Solve for h.
H=5.09684