you find that it takes a horizontal force of 160 newtons to slide a box along the surface of a level floor at constant speed . the coefficient of static friction is 0.52, and the coefficient of kinetic friction is 0.47. if you place the box on a dolly of mass 5.3 kg and with coefficient of rolling friction 0.018, what horizontal acceleration would that 160 newtons force provide?
To determine the horizontal acceleration provided by the 160 Newton force, we need to consider the forces acting on the box and the dolly.
1. Start by calculating the frictional force acting on the box when it is sliding at a constant speed. We can use the formula:
Frictional force = coefficient of kinetic friction * Normal force
The normal force is equal to the weight of the box, which can be calculated as the product of the mass and the acceleration due to gravity (9.8 m/s^2).
Mass of the box = Unknown
coefficient of kinetic friction = 0.47
Normal force = mass * gravity = Unknown * 9.8 m/s^2
2. The frictional force acting on the box is equal to the force you applied (160 Newtons). Therefore, we can set up an equation:
Frictional force = Applied force
0.47 * (Unknown * 9.8) = 160
3. Solve for the unknown mass by rearranging the equation:
Unknown * 9.8 = 160 / 0.47
Unknown = (160 / 0.47) / 9.8
Calculate the unknown mass.
4. Now, consider the forces acting on the dolly. The only significant force is the force of rolling friction, which can be calculated using the formula:
Rolling frictional force = rolling coefficient of friction * Normal force
The normal force acting on the dolly is equal to its weight, which can be calculated as the product of its mass and the acceleration due to gravity.
Mass of the dolly = 5.3 kg
Rolling coefficient of friction = 0.018
Normal force = mass * gravity = 5.3 kg * 9.8 m/s^2
5. Calculate the rolling frictional force:
Rolling frictional force = 0.018 * (5.3 * 9.8)
6. Now, we can determine the net force acting on the system (box + dolly) by subtracting the rolling frictional force from the applied force:
Net force = Applied force - Rolling frictional force
7. Finally, we can calculate the acceleration of the system using Newton's second law:
Net force = mass of box + mass of dolly * acceleration
Rearrange the equation to solve for acceleration:
Acceleration = Net force / (mass of box + mass of dolly)
Substitute the values and calculate the acceleration.
To find the horizontal acceleration provided by the 160 Newtons force, we first need to calculate the net force acting on the box. This requires considering the different types of friction involved.
1. Static Friction:
When the box is at rest, static friction acts to prevent the box from moving. The magnitude of static friction can be calculated using the equation:
Static Friction = Coefficient of Static Friction × Normal Force
In this case, the normal force is equal to the weight of the box, which can be calculated using:
Weight = mass × acceleration due to gravity
The coefficient of static friction is given as 0.52. Therefore, the static friction acting on the box is:
Static Friction = 0.52 × Normal Force
2. Kinetic Friction:
Once the box starts moving, the static friction is replaced by kinetic friction. The magnitude of kinetic friction can be calculated using the equation:
Kinetic Friction = Coefficient of Kinetic Friction × Normal Force
In this case, the coefficient of kinetic friction is given as 0.47. Therefore, the kinetic friction acting on the box while it is moving is:
Kinetic Friction = 0.47 × Normal Force
3. Rolling Friction:
When the box is placed on a dolly, rolling friction comes into play. The magnitude of rolling friction can be calculated using the equation:
Rolling Friction = Coefficient of Rolling Friction × Normal Force
In this case, the coefficient of rolling friction is given as 0.018, and the normal force acting on the dolly is equal to its weight, which can be calculated using:
Weight = mass of the dolly × acceleration due to gravity
With all these calculations, you can then find the net force acting on the box and divide it by the sum of the box's mass and the dolly's mass to obtain the horizontal acceleration.
Let M be the mass of the box.
160=M*.47g so you have M.
160=(M+5.3)g*.018)a
solve for a.