A child is sitting on a stationary skateboard with a pile of rocks which she throws in one direction in order to make the skateboard travel in the opposite direction. If the rocks each have a mass of 0.95 kg and she can throw them with a speed of 19 m/s relative to the ground, determine the number of rocks she must throw per minute in order to maintain a constant average speed against a 3.4 N force of friction. (Note: because this is a rate, the answer may not be a whole number.)
Let K be number rocks minute
K*min/60sec*velocity*mass=force
3.4N=K/60sec/min *19m/s*.95kg
but N=kg*m/s^2
K=3.4kg*m/s^2 *60s/min*1/(19m/s*.95kg)
K=3.4*60/(19*.95) rocks/min
=about 11 rocks/min check that.
To determine the number of rocks the child must throw per minute, we need to first calculate the total momentum change required per minute to counterbalance the friction force.
Step 1: Calculate the momentum change per rock:
The momentum change per rock can be calculated using the formula:
Δp = 2m∆v
where Δp is the change in momentum, m is the mass of the rock, and ∆v is the change in velocity.
Given:
m (mass of each rock) = 0.95 kg
∆v (change in velocity) = 19 m/s
Using the formula, the momentum change per rock is:
Δp = 2 * 0.95 kg * 19 m/s = 36.1 kg*m/s
Step 2: Calculate the number of rocks thrown per minute:
To maintain a constant average speed, the momentum change required per minute must counterbalance the friction force acting on the skateboard. The total momentum change per minute is given by the formula:
Total Δp = F * t
where F is the friction force and t is the time.
Given:
F (friction force) = 3.4 N
Total Δp = 3.4 N * t (since momentum change = force * time)
We want to find t (time) for which the momentum change is equal to the total Δp required, which is the momentum change per rock * number of rocks thrown per minute:
Total Δp = Δp * n
Where n is the number of rocks thrown per minute.
Combining the two equations:
3.4 N * t = 36.1 kg*m/s * n
We need to solve for n, the number of rocks thrown per minute. Rearranging the equation:
n = (3.4 N * t) / (36.1 kg*m/s)
Step 3: Calculate the number of rocks:
To determine the number of rocks, we need to know the time it takes for the child to throw the rocks per minute. Assuming it takes x minutes to throw the rocks:
n = (3.4 N * x minutes) / (36.1 kg*m/s)
Therefore, the number of rocks she must throw per minute in order to maintain a constant average speed against a 3.4 N force of friction is given by the equation:
n = (3.4 * x) / 36.1 rocks/minute
The answer will depend on the value of x.
To determine the number of rocks the child must throw per minute, we need to calculate the force exerted by throwing each rock and then divide the force of friction by that value.
First, let's calculate the momentum change of the skateboard when one rock is thrown. The momentum change can be calculated using the equation:
Δp = m * Δv
where Δp is the change in momentum, m is the mass of the rock, and Δv is the change in velocity.
Since the skateboard and the child are initially at rest, the momentum change of the skateboard can be determined by the equation:
Δp = -m * V
where V is the velocity at which the rock is thrown relative to the ground.
Using these equations, we can calculate the force exerted by throwing each rock:
F = Δp / Δt
where Δp is the change in momentum and Δt is the time taken to throw one rock.
Now, let's calculate the force of friction:
Ffriction = µ * N
where µ is the coefficient of friction and N is the normal force. Since the skateboard is stationary, the normal force N is equal to the weight of the child.
Finally, we can determine the number of rocks the child must throw per minute:
Number of rocks per minute = Ffriction / F
Let's plug in the given values to calculate the answer.
Given:
m = 0.95 kg (mass of each rock)
V = 19 m/s (velocity at which the rock is thrown relative to the ground)
Ffriction = 3.4 N (force of friction)
First, we need to calculate the force exerted by throwing each rock:
Δp = -m * V
Δp = -0.95 kg * 19 m/s
Δp = -18.05 kg·m/s
Next, we calculate the force:
F = Δp / Δt
To find Δt, we need to know the time it takes the child to throw one rock. Since this information is not provided, let's assume it takes 1 second to throw one rock.
Δt = 1 s
Now we can calculate the force:
F = -18.05 kg·m/s / 1 s
F = -18.05 N
Note that the force is negative because it acts in the opposite direction of the thrown rock.
Now, let's calculate the number of rocks the child must throw per minute:
Number of rocks per minute = Ffriction / F
Number of rocks per minute = 3.4 N / 18.05 N
Number of rocks per minute = 0.187 rocks per minute (approximately)
Therefore, the child must throw approximately 0.187 rocks per minute to maintain a constant average speed against the 3.4 N force of friction.