A child's toy car runs off a battery that can supply 105 Wh of energy. If all losses (including friction) consume 45.0% of the energy available and the rider and car have a combined weight of 910 N, determine the height of the largest hill the child can climb in the car in a hilly terrain.
mgh=.55*105W*3600sec
mg=910
h= you solve it.
To determine the height of the largest hill the child can climb, we need to calculate the available energy after accounting for losses and then convert that energy into potential energy.
First, let's calculate the available energy after losses. We know that losses consume 45.0% of the total energy.
Total energy provided by the battery = 105 Wh
Energy consumed by losses = 45.0% of 105 Wh
To calculate the energy consumed by losses:
Energy consumed by losses = (45.0 / 100) * 105 Wh
Now, let's calculate the available energy for climbing the hill:
Available energy = Total energy - Energy consumed by losses
Next, we need to convert the available energy into potential energy to determine the maximum height the child can climb.
Potential energy = m * g * h
Where:
m = mass (in kg)
g = acceleration due to gravity (9.8 m/s^2)
h = height (in meters)
But we are given the weight (910 N), not the mass, so we need to convert it to mass using Newton's second law:
Weight = mass * acceleration due to gravity
910 N = m * 9.8 m/s^2
Solving for mass (m):
m = 910 N / 9.8 m/s^2
Now that we have the mass, we can calculate the height of the largest hill:
Potential energy = Available energy
m * g * h = Available energy
Solving for h (height):
h = Available energy / (m * g)
Now, let's put the values into the formula and calculate the height.