A 1500kg car moving at a speed of 20 m/s comes to a halt. How much work was done by the brakes?
How fast can a 2.0 horsepower motor lift a 200 kg mass?
A boy with a mass of 20 kg is riding on a 10 kg cart which is travelling at 3 m/s. He jumps off in such a way that he lands on the ground with no horizontal speed. What was the change of speed of the cart?
not sure how to solve please help
1. Work = 0.5M*V^2 = 0.5*1500*20^2 =
300,000 J.
2. hp * 746W/hp = 1492 Watts=1492J/s.
P = F*V = Mg * V = 1492 J/s.
200*9.8 * V = 1492
1960V = 1492
V = 0.76 m/s.
thank you for the help
Glad I could help.
To solve these physics problems, we need to apply the relevant equations and principles. Let's tackle each question step by step:
1. How much work was done by the brakes?
The work done by the brakes can be calculated using the work-energy principle. The formula for work is:
Work = Force x Distance x Cos(θ)
Since the car comes to a halt, the work done by the brakes is equal to the initial kinetic energy of the car. The formula for kinetic energy is:
KE = 0.5 x mass x velocity^2
Substituting the given values:
KE = 0.5 x 1500 kg x (20 m/s)^2
Calculating the kinetic energy will give you the work done by the brakes.
2. How fast can a 2.0 horsepower motor lift a 200 kg mass?
First, convert the horsepower to watts. 1 horsepower is equal to 746 watts. So, a 2.0 horsepower motor can produce:
Power = 2.0 horsepower x 746 watts/horsepower
Now, use the work-energy principle. The work done by the motor is equal to the change in potential energy due to lifting the mass. The formula for work is:
Work = Force x Distance x Cos(θ)
Since the motor is lifting the object vertically, the angle between the force and displacement is 0 degrees, which means Cos(θ) = 1.
The work done by the motor is given by:
Work = m x g x h
Where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height the mass is lifted.
Equating the work done by the motor to the power output of the motor, you can calculate the height the mass can be lifted.
3. What was the change of speed of the cart?
This question deals with the conservation of momentum. Initially, the momentum of the system (boy + cart) is calculated by multiplying the mass of the system by its velocity. At the end, when the boy jumps off, the momentum of the system becomes the momentum of the cart alone.
Momentum (initial) = (Mass of boy + Mass of cart) x Velocity (initial)
Momentum (final) = Mass of cart x Velocity (final)
The change in momentum is the difference between these two values, and the change in velocity is the change in momentum divided by the mass of the cart.