A student pushes stright along the handles of a mower with a force of 200 N. The handles make a angle of 20°, with respect to the horizontal. The frictional force for the 25 kg mower is 100 N. What is the normal force on the mower, and what is the acceleration of the mower?
The normal(downward vertical)force on the mower is M*g + F*sin20 = 245 + 34.2 = 279.2 N
It is balanced by a vertical upward force from the ground.
The acceleration is the net forward force divided by the mass.
a = [(200 cos20) -100]/25 = 3.52 m/s^2
I doubt if the mower can sustain that acceleration rate for very long. After 3 seconds he would be moving faster than Usain Bolt.
To find the normal force on the mower, we need to consider the vertical forces acting on it. Since the mower is on a horizontal surface, the normal force and the gravitational force will be equal in magnitude and opposite in direction.
1. Calculate the gravitational force acting on the mower:
F_gravity = m * g
where m is the mass of the mower (25 kg) and g is the acceleration due to gravity (9.8 m/s^2).
F_gravity = 25 kg * 9.8 m/s^2 = 245 N
2. Determine the normal force:
The normal force (F_normal) will be equal to the gravitational force, but in the opposite direction.
F_normal = - F_gravity = - 245 N (since it opposes the gravitational force)
Next, to find the acceleration of the mower, we need to consider the horizontal forces acting on it.
3. Resolve the force applied by the student along and perpendicular to the horizontal direction:
The force applied (F_applied) can be decomposed into two components:
F_parallel = F_applied * cos(angle)
F_perpendicular = F_applied * sin(angle)
where the angle is 20°.
F_parallel = 200 N * cos(20°) = 200 N * 0.9397 = 187.94 N (rounded to two decimal places)
F_perpendicular = 200 N * sin(20°) = 200 N * 0.3420 = 68.40 N (rounded to two decimal places)
4. Calculate the net force in the horizontal direction:
The net force (F_net) is the difference between the applied force parallel to the horizontal direction and the frictional force.
F_net = F_parallel - F_friction = 187.94 N - 100 N = 87.94 N (rounded to two decimal places)
5. Determine the acceleration:
Using Newton's second law of motion (F_net = m * a), we can find the acceleration (a) of the mower.
a = F_net / m
a = 87.94 N / 25 kg = 3.52 m/s^2 (rounded to two decimal places)
Therefore, the normal force on the mower is -245 N (opposite to the gravitational force) and the acceleration of the mower is 3.52 m/s^2.
To find the normal force on the mower, we need to consider the forces acting on the mower in the vertical direction.
The forces acting on the mower in the vertical direction are the weight of the mower and the normal force. The weight of the mower is given by the formula:
Weight = mass * gravity
In this case, the mass of the mower is given as 25 kg and the acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the weight of the mower is:
Weight = 25 kg * 9.8 m/s^2 = 245 N
Since the mower is on a horizontal surface and not accelerating in the vertical direction, the normal force must be equal to the weight of the mower. So, the normal force on the mower is also 245 N.
Now, to find the acceleration of the mower, we need to consider the forces acting on it in the horizontal direction.
The forces acting on the mower in the horizontal direction are the pushing force and the frictional force. The pushing force has a horizontal component and a vertical component. The horizontal component of the pushing force is given by:
Pushing force horizontal component = Pushing force * cos(angle)
In this case, the pushing force is given as 200 N and the angle is 20°. Therefore, the horizontal component of the pushing force is:
Pushing force horizontal component = 200 N * cos(20°) ≈ 189.54 N
The frictional force acts in the opposite direction to the horizontal component of the pushing force. Therefore, its value is given as -100 N (negative because it opposes the motion).
Now, we can calculate the net force acting on the mower in the horizontal direction:
Net force = Pushing force horizontal component - Frictional force
= 189.54 N - 100 N
= 89.54 N
Finally, we can use Newton's second law (F = ma) to find the acceleration of the mower:
Net force = mass * acceleration
Rearranging the equation, we have:
acceleration = Net force / mass
= 89.54 N / 25 kg
≈ 3.58 m/s^2
Therefore, the normal force on the mower is 245 N and the acceleration of the mower is approximately 3.58 m/s^2.