A father skating pushes a baby in a cart over a distance of 100m. The father starts from rest and wants to reach a speed of 5.0m/s, How hard does the father need to push in the direction of the motion? The cart has a mass of 10.0kg and the baby is 8.0kg.
Wouldn't it depend on friction? Of course it depends on friction.
Now if one were to disregard friction, as on ice, of course dad could not push the cart at all. Ignoring even that..
netforce=mass*acceleration or a=F/m
vf^2=vi^2+2ad=vi^2+2(F/m)d solve for force F.
oh sorry forgot the important part LOL uhm it says to NEGLECT friction
To determine the force the father needs to exert in order to push the baby in the cart over a distance of 100m, we can break down the problem into several steps.
Step 1: Calculate the total mass
To find the total mass, we add the mass of the cart and the mass of the baby:
Total mass = mass of cart + mass of baby = 10.0 kg + 8.0 kg = 18.0 kg
Step 2: Calculate the acceleration
Using the formula for acceleration, we can calculate the acceleration required to go from rest to a speed of 5.0 m/s over a distance of 100m:
Acceleration = (final velocity - initial velocity) / time
Since the father starts from rest, the initial velocity is 0:
Acceleration = (5.0 m/s - 0 m/s) / t
We do not know the time it takes, so let's call it "t" for now.
Step 3: Calculate the force required
Using Newton's second law of motion, we can calculate the force required to accelerate the system:
Force = mass x acceleration
Force = 18.0 kg x acceleration
Step 4: Solve for acceleration
To solve for acceleration, we can use the formula:
Distance = (initial velocity x time) + (0.5 x acceleration x time^2)
Plugging in the given values:
100m = (0 x t) + (0.5 x acceleration x t^2)
100m = 0.5 x acceleration x t^2
Rearranging the equation, we get:
acceleration = (100m / (0.5 x t^2))
Step 5: Final calculation
Now that we have the acceleration, we can substitute it back into the equation for force:
Force = 18.0 kg x acceleration
To summarize the steps:
1. Calculate the total mass: Total mass = mass of cart + mass of baby
2. Calculate the acceleration: Acceleration = (final velocity - initial velocity) / time
3. Calculate the force required: Force = mass x acceleration
4. Solve for acceleration: Distance = (initial velocity x time) + (0.5 x acceleration x time^2)
5. Substitute the acceleration back into the equation for force: Force = 18.0 kg x acceleration
By following these steps, you can calculate the force that the father needs to exert in the direction of motion to push the baby in the cart over a distance of 100m.