Calculating Accelerations of Block & Toboggan on Ice

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In summary, to calculate the accelerations of the block and toboggan in this scenario, you can use Newton's Second Law and the equations for friction and weight. The net force acting on each object can be calculated by considering the pull force, friction force, and weight, and then substituted into the equation Fnet = ma to determine the acceleration.
  • #1
NKKM
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HI,
I am confused about how to approach this question.

A 4.0 kg toboggan rests on a frictionless icy surface, and a 2.0 kg block rests on
top of the toboggan. The coefficient of static friction m
s between the block and the surface of the toboggan is 0.60, whereas the kinetic friction coefficient is 0.51. The block is pulled by a 30 N-horizontal force as shown. What are the magnitudes and directions of the resulting accelerations of the block and the toboggan?

If I calculate the acceleration of the box as so: Fpull- Ffriction = Fnet = ma
using the kinetic friction coefficient and solve for acceleration. Does that make sense.. and how then do I approach the acceleration of the toboggan?
 
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  • #2
To calculate the acceleration of the block and the toboggan, you can use Newton's Second Law. The net force acting on the block is the sum of the pull force and the friction force. This force will cause an acceleration of the block, which can be calculated using the equation: Fnet = ma, where m is the mass of the block and a is the acceleration. The friction force acting on the block can be calculated by multiplying the coefficient of kinetic friction (0.51) with the normal force. The normal force is equal to the weight of the block, which can be calculated using the equation: Fg = mg, where m is the mass of the block and g is the acceleration due to gravity (9.81 m/s2). Thus, you can calculate the acceleration of the block by substituting the calculated friction force and the pull force into the equation: Fpull + Ffriction = ma. The acceleration of the toboggan can also be calculated using Newton's Second Law. The net force acting on the toboggan is the sum of the pull force and the friction force. The friction force acting on the toboggan can be calculated by multiplying the coefficient of static friction (0.60) with the normal force. The normal force is equal to the sum of the weight of the toboggan and the weight of the block, which can be calculated using the equation: Fg = mg, where m is the mass of the combined system and g is the acceleration due to gravity (9.81 m/s2). Thus, you can calculate the acceleration of the toboggan by substituting the calculated friction force and the pull force into the equation: Fpull + Ffriction = ma. I hope this helps!
 
  • #3


I would approach this question by first identifying all the given information and variables. This includes the masses of the toboggan and block, the coefficients of friction, and the applied force of 30 N.

Next, I would use Newton's second law of motion (F=ma) to calculate the acceleration of the block. Using the kinetic friction coefficient, I would subtract the force of friction from the applied force to determine the net force acting on the block. This net force can then be divided by the mass of the block to determine its acceleration.

For the toboggan, we can use the fact that it is on a frictionless surface to determine that there is no horizontal force acting on it. Therefore, the only force acting on the toboggan is the normal force from the block. We can use the same equation (F=ma) and the mass of the toboggan to calculate its acceleration.

To determine the direction of the accelerations, we can use the fact that the applied force is horizontal, and therefore the resulting acceleration will also be horizontal in the same direction. The direction of the friction force will depend on the direction of the applied force and the coefficient of friction.

In summary, to calculate the accelerations of the block and toboggan, we can use Newton's second law and the given information about mass and friction coefficients. It is important to keep track of the direction of the forces and to use the correct friction coefficient (kinetic or static) depending on the situation.
 

1. How do you calculate the acceleration of a block and toboggan on ice?

To calculate the acceleration of a block and toboggan on ice, you will need to use the formula a = (Fnet - Ff)/m, where a is the acceleration, Fnet is the net force, Ff is the force of friction, and m is the mass of the block and toboggan.

2. What is the force of friction in this scenario?

The force of friction is the force that opposes the motion of the block and toboggan on the icy surface. It is dependent on the coefficient of friction between the ice and the objects, as well as the normal force acting on the objects.

3. How do you measure the coefficient of friction on ice?

The coefficient of friction on ice can be measured through experiments where the force required to move an object across the ice is measured and divided by the normal force acting on the object. This will give you the coefficient of friction for the specific surface and objects being tested.

4. How does the mass of the block and toboggan affect the acceleration on ice?

The mass of the block and toboggan will affect the acceleration on ice as it is a factor in the calculation of acceleration. The larger the mass, the greater the force of friction and the smaller the acceleration, and vice versa.

5. What other factors can impact the acceleration of a block and toboggan on ice?

Other factors that can impact the acceleration of a block and toboggan on ice include the angle of the slope, the shape and size of the objects, and any external forces acting on the objects such as wind or an incline.

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