A 10kg block is sliding at 10m/s along a frictionless track which suddenly curves straight up. how high will the block rise
The initial KE is 1/2 m v^2.
That energy goes into PE, mgh.
set mgh equal to 1/2 mv^2, solve h.
h= 1/2 v^2/g I think,check that.
To determine how high the block will rise after curving straight up, we need to consider the conservation of mechanical energy.
First, let's calculate the initial kinetic energy (KEi) of the block. The formula for kinetic energy is KE = (1/2) * mass * velocity^2.
Given:
Mass (m) = 10 kg
Velocity (v) = 10 m/s
KEi = (1/2) * m * v^2
KEi = (1/2) * 10 kg * (10 m/s)^2
KEi = (1/2) * 10 kg * 100 m^2/s^2
KEi = 500 J (Joules)
As the block curves straight up, its kinetic energy will convert to potential energy (PE) as it gains height. The formula for potential energy is PE = mass * gravity * height.
Given:
Mass (m) = 10 kg
Gravity (g) = 9.8 m/s^2 (approximate value on Earth)
PE = m * g * h
Since the block starts from rest at its highest point (when it momentarily stops before descending), its final velocity is 0 m/s. Therefore, all the initial kinetic energy will be converted to potential energy.
PE = KEi
m * g * h = 500 J
Rearranging the equation to solve for height (h):
h = 500 J / (m * g)
h = 500 J / (10 kg * 9.8 m/s^2)
h = 5.1 meters
Therefore, the block will rise approximately 5.1 meters.