Question

After a heavy snowfall, Annie wants to drag a sled loaded with toys across her level backyard floor, by pulling a rope at an angle of 26 degrees up from the snowy floor. When Annie increases her pull to 25N, the sled starts. Two days later, all the snow has melted leaving the concrete exposed. Annie pulls on the loaded sled, but now it has become harder to get it to start. Annie does not want to change the pulling angle, because it is most natural for her. Answer the 3 parts:

a) Draw a free body diagram for Annie's sled, labeling forces

b) The coefficients of static friction for snow and concrete are 0.15 and 0.95, respectively. How large is the normal force of the floor in the two cases (snow and concrete)?

c) How much mass does Annie need to remove from the sled, to be able to start the sled on the concrete by pulling just as hard as she did earlier on the snow?

Answer 1

Given is:-

Angle of inclination = 26 degrees

Pulling Force = 25N

Friction of coefficients,

For snow = 0.15

For concrete = 0.95

Part-a

The free body diagram of the given problem labelling all the forces is given below.

Part-b

The normal force is the force which is exerted by the floor onto the object according to the newton's third law of motion.

It only depends upon the mass of the object (because acceleration due to gravity is fix near earth's surface = g =9.8 m/s^2) therefore we can say that it is not depend upon the type of surface or the coefficient of friction.

Hence the normal force exerted by earth on the Annie in both cases will be of same magnitude.

Part-c

Initially when snow is there

the Frictional force + Force due to gravity = 25N

by putting all the values in above equation, we get

Initially the weight of annie and her toys is 4.448 Newtons.

Now for concrete

or

So she has to reduce the force by 56-25 = 31N (because she wants to pull with same force as previous)

therefore the mass she has to reduce will be

Hence she has to reduce 3.16 kg of toys