# T2 practice (Spring 2008) ```TEST 2 Practice Problems
Newton’s 2nd law
1. A pilot flies an airplane in a vertical circular loop at a constant speed υ = 160 m/s. If the
pilot’s apparent weight at the top of the loop is one-third of his true weight when he is on
the ground, find the radius R of the plane’s circular path.
Ans: 1960 m
2. A small 8 Kg sphere is tied to two strings and spins horizontally around
the vertical rod with θ = 36.87&deg; as shown. If the frequency of the sphere’s
circular motion is 1.2 rev/s, find the tension force in the horizontal string.
Use cos36.87&deg; = 0.8 and sin36.87&deg; = 0.6.
Ans: 77.6 N
3. A block is placed inside the spinning cone as
shown. Given L = 0.5 m, μs = 0.3, and β = 36.87˚,
find the minimum rotating frequency f of the cone
that will keep the block from slipping. Use
cos36.87&deg; = 0.8 and sin36.87&deg; = 0.6.
Ans: 0.477 rev/s
μs
β
L
F
36.87&deg;
μk
B
B
μk = 0.2
A
μk = 0.25
36.87˚
0.5 m
f
4. The 10 Kg block slides on the horizontal floor as
the pulling force F = 30 N is applied on the cable as
shown. If the acceleration of the block is 7.2 m/s2,
find the coefficient of friction μk between the block
and the floor. Use cos36.87˚ = 0.8 and sin36.87˚ =
0.6.
Ans: 0.15
5. Two blocks A (mA = 20 Kg) and B
(mB = 15 Kg) are connected by a cable
passing over a pulley, and a force F is
applied pulling block B as shown. The
coefficients of friction are μk = 0.25
between A and the ramp and μk = 0.2
between B and the horizontal floor. If
block A slides up along the incline with
an acceleration a = 0.56 m/s2, find the
pulling force F. Use cos36.87&deg; = 0.8
and sin36.87&deg; = 0.6.
Ans: 103 N
θ
F
```