a skater with a mass of 65kg,reaches the bottom of a ramp ,2.5 metres high ,going at 27km.h-1.
calculate his kinetic energy as he reaches the ramp
calculate how fast he is going by the time he reaches the top of the ramp
I am sure that you could have done this problem three times in the time you spent typing it.
v = 27 km/hr * 1000m/km * 1 hr/3600 s
Ke = (1/2) m v^2
loss of energy = m g h
Ke at top = Ke at bottom i energy lost
(1/2) m u^2 = Ke at top
Ke at top = Ke at bottom - energy lost
To calculate the kinetic energy of the skater as they reach the bottom of the ramp, we can use the following formula:
Kinetic Energy = (1/2) * m * v^2
where:
m = mass of the skater = 65 kg
v = velocity of the skater
First, we need to convert the velocity from km/h to m/s since the unit for kinetic energy is joules (J). There are 3.6 seconds in 1 hour, so to convert km/h to m/s, we divide by 3.6:
27 km/h รท 3.6 = 7.5 m/s (rounded to one decimal place)
Now we can substitute the values into the formula:
Kinetic Energy = (1/2) * 65 kg * (7.5 m/s)^2
= (1/2) * 65 kg * 56.25 m^2/s^2
= 1,828.125 J (rounded to three decimal places)
Therefore, the skater's kinetic energy as they reach the bottom of the ramp is 1,828.125 joules.
To calculate how fast the skater is going by the time they reach the top of the ramp, we need to use the Law of Conservation of Energy. As the skater moves up the ramp, their kinetic energy is converted into potential energy. At the top of the ramp, all the kinetic energy is converted into potential energy.
The potential energy is given by:
Potential Energy = m * g * h
where:
m = mass of the skater = 65 kg
g = acceleration due to gravity = 9.8 m/s^2
h = height of the ramp = 2.5 m
Substituting the values:
Potential Energy = 65 kg * 9.8 m/s^2 * 2.5 m
= 1,602.5 J (rounded to one decimal place)
Since the skater's kinetic energy is converted into potential energy, the kinetic energy at the top of the ramp is zero. Therefore, the skater is momentarily stationary at the top of the ramp.
In conclusion, the skater's kinetic energy as they reach the bottom of the ramp is 1,828.125 joules, and they are momentarily stationary at the top of the ramp.