a worker pushes a 7kg shipping box along a roller track. assume friction is small enough to be ignored because of the rollers. the worker's push is 25 N directed down and to the right at an angle of 20 degrees.
1. determine the horizontal component of the worker's push
2. write a net force equation for the horizontal forces on the box
3. determine the acceleration of the box
4. determine the normal force on the box
1. The horizontal component of the worker's push is 21.2 N.
2. Net force equation for the horizontal forces on the box: Fnet = 25cos(20°) - Ff = 25cos(20°) = 21.2 N.
3. Acceleration of the box: a = Fnet/m = 21.2 N/7 kg = 3 m/s2.
4. Normal force on the box: Fnormal = Fnet/sin(20°) = 25/sin(20°) = 28.3 N.
1. To determine the horizontal component of the worker's push, we can use trigonometry. The horizontal component can be found using the equation:
Horizontal Component = Magnitude of Force * cos(angle)
Plugging in the values, we get:
Horizontal Component = 25 N * cos(20 degrees)
Horizontal Component ≈ 23.94 N
Therefore, the horizontal component of the worker's push is approximately 23.94 N.
2. To write the net force equation for the horizontal forces on the box, we need to consider all the forces acting in the horizontal direction. In this case, there are only two forces: the horizontal component of the worker's push and the friction force (which is ignored).
Therefore, the net force equation for the horizontal forces on the box is:
Net Force = Horizontal Component - Friction Force
Since the friction force is ignored, the equation can be simplified as:
Net Force = Horizontal Component
So, in this case, the net force equals the horizontal component of the worker's push, which is approximately 23.94 N.
3. To determine the acceleration of the box, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. The equation can be written as:
Net Force = Mass * Acceleration
We can rearrange this equation to solve for acceleration:
Acceleration = Net Force / Mass
Plugging in the values, we get:
Acceleration = 23.94 N / 7 kg
Acceleration ≈ 3.42 m/s^2
Therefore, the acceleration of the box is approximately 3.42 m/s^2.
4. The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the box is resting on a surface with rollers, so the normal force will be equal in magnitude and opposite in direction to the weight of the box.
The weight of the box can be calculated using the equation:
Weight = mass * acceleration due to gravity
Plugging in the values, we get:
Weight = 7 kg * 9.8 m/s^2
Weight ≈ 68.6 N
Therefore, the normal force on the box is approximately 68.6 N.
1. To determine the horizontal component of the worker's push, we need to find the component of the force that acts in the horizontal direction. We can use trigonometry to find this component.
The horizontal component of the force can be calculated using the formula: horizontal component = force * cosine(angle).
Given that the force applied by the worker is 25 N and the angle is 20 degrees, we can plug in these values into the formula:
Horizontal component = 25 N * cos(20 degrees)
Horizontal component = 25 N * 0.9397
Horizontal component ≈ 23.49 N
Therefore, the horizontal component of the worker's push is approximately 23.49 N.
2. To write the net force equation for the horizontal forces on the box, we need to consider all the forces acting horizontally on the box. In this case, the only horizontal force acting on the box is the horizontal component of the worker's push.
Net Force (horizontal) = Horizontal component of worker's push
Therefore, the net force equation for the horizontal forces on the box is:
Net Force (horizontal) = 23.49 N (since the horizontal component of the worker's push is approximately 23.49 N)
3. To determine the acceleration of the box, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
The formula for acceleration is given by: acceleration = net force / mass.
In this case, the mass of the box is 7 kg, and the net force acting on it is the horizontal component of the worker's push, which is 23.49 N.
Acceleration = 23.49 N / 7 kg
Acceleration ≈ 3.35 m/s^2
Therefore, the acceleration of the box is approximately 3.35 m/s^2.
4. To determine the normal force on the box, we need to consider the vertical forces acting on the box. In this case, the only vertical force acting on the box is its weight.
The weight of an object can be calculated using the formula: weight = mass * acceleration due to gravity.
Given that the mass of the box is 7 kg, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight:
Weight = 7 kg * 9.8 m/s^2
Weight ≈ 68.6 N
Therefore, the normal force on the box is approximately 68.6 N, as it is equal and opposite to the weight of the box.