A 33 kg lawnmower is pulled by a 100N force on flat ground. The handle makes a 10º angle with the ground.The coefficient of friction between the grass and lawnmower wheels is 0.10. What is the normal force, force of friction and the acceleration? please provide step by step solutions
33 kg lawnmower is pulled by a 100N force on flat ground. The handle makes a 10º angle with the ground. The coefficient of friction between the grass and lawnmower wheels is 0.10.
a. Calculate the normal force.
b. Calculate the force of friction.
c. Calculate the acceleration.
Please add step by step solutions with answer
Salim has a paper route. In the winter time, he puts his newspapers on a toboggan to pull them through the snow. The combined mass of the papers and the toboggan is 24 kg. The coefficient of static friction between the toboggan and the snow is 0.18. The coefficient of kinetic friction between the toboggan and the snow is 0.10.
a. With how much force must Salim pull in order to get the toboggan to start moving?
b. How much force is needed to keep the toboggan moving at a constant speed? Please can I get a step by step solution and answer
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To solve this problem, we will break it down into steps:
Step 1: Determine the normal force.
The normal force is the perpendicular force exerted by a surface to support the weight of an object resting on it. In this case, the weight of the lawnmower is acting downward, and the normal force opposes it in the upward direction. Since the lawnmower is on flat ground, the normal force is equal in magnitude and opposite in direction to the weight.
Normal force = weight of the lawnmower = mass × gravity
Normal force = 33 kg × 9.8 m/s²
Normal force = 323.4 N
Step 2: Determine the force of friction.
The force of friction can be calculated using the coefficient of friction and the normal force. In this case, the force of friction opposes the pulling force applied to the lawnmower.
Force of friction = coefficient of friction × normal force
Force of friction = 0.10 × 323.4 N
Force of friction = 32.34 N
Step 3: Determine the horizontal component of the applied force.
The pulling force applied to the lawnmower has two components: a vertical component and a horizontal component. We are only concerned with the horizontal component because it affects the acceleration.
Horizontal component of force = applied force × cos(angle)
Horizontal component of force = 100 N × cos(10º)
Horizontal component of force ≈ 98.53 N
Step 4: Calculate the net force.
The net force is the sum of the horizontal forces acting on the lawnmower. In this case, the applied force and the force of friction contribute to the net force.
Net force = horizontal component of force - force of friction
Net force = 98.53 N - 32.34 N
Net force ≈ 66.19 N
Step 5: Determine the acceleration.
The acceleration can be calculated using Newton's second law, which states that the acceleration of an object is directly proportional to the net force and inversely proportional to its mass.
Acceleration = net force / mass
Acceleration = 66.19 N / 33 kg
Acceleration ≈ 2.00 m/s²
To summarize:
- The normal force is 323.4 N.
- The force of friction is 32.34 N.
- The acceleration is approximately 2.00 m/s².