Cathy takes the bus home from work. In her hand she holds a 2 kg cake box, tied together with a string. As she ascends the steps into the bus,the box accelerates upward at a rate of 2.5m/s^2. what is the force exerted on the string?
Fg=ma
=2*9.8
=19.6N
Fn=ma-Fg
=2*2.5-(-19.6)
=24.6N
b)she sets the box on the seat beside her. the bus acelerates from rest to 60 km/h in 4 s and the box begins to slide. What's the coefficient ofstatic friction b/w the box and te bus seat?
Ff=m*Fn
=2(24.6)
=49.2N
static coefficient=Ff/Fn
=49.2/24.6
=2
c)a taxi suddenly cuts infront of the bus, causing the bus driver to slam on the brakes. The bus driver reduces the speed from 60 km/h to 20 km/h in 1.5 s. Does Cathy's cake slide forward?
I have no idea how to even start with this one.
I am taking this course and am confused with this question... in the second part to(a),why does 19.6 become negative to get 24.6?
If it accelerating upward wouldn't 19.6 be positive making the answer
2(2.5)-19.6
=-14.6N
???
To determine if Cathy's cake will slide forward, we need to compare the force of friction acting on the cake with the force required to overcome static friction. If the force required to overcome static friction is greater than or equal to the force of friction, the cake will not slide forward.
To do this, we first need to calculate the force of friction acting on the cake during the braking.
The initial velocity (vi) of the bus is 60 km/h, which needs to be converted to m/s:
vi = 60 km/h * (1000 m/km) / (3600 s/h) = 16.67 m/s
The final velocity (vf) of the bus is 20 km/h, which needs to be converted to m/s:
vf = 20 km/h * (1000 m/km) / (3600 s/h) = 5.56 m/s
The time taken to decelerate (t) is given as 1.5 s.
Now, we can calculate the change in velocity (Δv):
Δv = vf - vi = 5.56 m/s - 16.67 m/s = -11.11 m/s (negative sign indicates deceleration)
Next, we can calculate the acceleration (a) during deceleration:
a = Δv / t = -11.11 m/s / 1.5 s = -7.41 m/s^2 (negative sign indicates deceleration)
Now, we can calculate the force of friction (Ff) acting on the cake while decelerating:
Ff = m * a
Given that the mass of the cake (m) is 2 kg:
Ff = 2 kg * (-7.41 m/s^2) = -14.82 N (negative sign indicates opposite direction of motion)
Since the force of friction is negative, it means it acts in the opposite direction to the motion, which in this case is forward.
Therefore, if the force of friction is greater than or equal to the force required to overcome static friction, then the cake will not slide forward.