Ankit asked 9 months ago
What minimum speed does a 100 g puck need to make it to the top of a 2.9-m-long, 34° frictionless ramp?
R K answered 9 months ago
Step No: 1
The diagram to calculate height of the ramp using the length of the ramp and inclination of the ramp is as follows:
A use full trigonometry ratio in a right angle triangle is,
sinθ=hypotonuse/oppositeside
sin34∘=2.9m/h
Solve for h.
h=(2.9m)sin34∘=1.62m
Step No: 2
The expression for kinetic energy K of a moving object of mass m is,
K=1/2mv2
The potential energy of an object which is at a height h above the reference level is,
U=mgh
The total energy of the puck at the bottom of the ramp is its kinetic energy. If this total kinetic energy is converted into total potential energy of the puck when it reaches the top of the ramp.
K=U
Substitute 1/2mv2 for K and mgh for U.
1/2mv2=mgh
1/2v2=gh
Rearrange the equation for v.
v=√2gh
Substitute 9.8m/s2 for g and 1.62 m for h.
v=√2(9.8m/s2)(1.62m)=5.64m/s