A man pushes his child in a grocery cart. The total mass of the cart and child is 30.0 kg. If the force of friction on the cart is 15.0 N, how hard does the man have to push so that the cart accelerates at 1.50 m/s/s?
F=ma, so 30.0 * 1.50 + 15.0 = 60.0N
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To find out how hard the man has to push, we can apply Newton's second law of motion, which states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration.
Step 1: Write down the given values:
Mass (m) = 30.0 kg
Friction force (F_friction) = 15.0 N
Acceleration (a) = 1.50 m/s^2
Step 2: Write down Newton's second law equation:
F_net = m * a
Step 3: Calculate the net force (F_net):
F_net = m * a
F_net = (30.0 kg) * (1.50 m/s^2)
F_net = 45.0 N
Step 4: Account for the force of friction:
The man needs to overcome the force of friction to make the cart accelerate. Since the force of friction acts in the opposite direction of motion, we subtract it from the net force.
Force exerted by the man (F_man) = F_net + F_friction
F_man = 45.0 N + 15.0 N
F_man = 60.0 N
Therefore, the man needs to push with a force of 60.0 N to make the cart accelerate at 1.50 m/s^2.
To find out how hard the man has to push the grocery cart, we can use Newton's second law of motion, which states that the force acting on an object is equal to the product of its mass and acceleration.
The formula for Newton's second law is:
F = m * a
Where:
F is the force applied to the cart
m is the mass of the cart and child combined
a is the acceleration of the cart
In this case, the mass of the cart and child is given as 30.0 kg, and the acceleration is given as 1.50 m/s/s. We need to solve for F.
F = (30.0 kg) * (1.50 m/s/s)
F = 45.0 N
Therefore, the man has to push the cart with a force of 45.0 Newtons in order to achieve an acceleration of 1.50 m/s/s.