Question

force and acceleration

1. skelly the skater, total mass 25 kg, is propelled by rocket power.

a. complete table i
(neglect resistance)
table i
b. complete table ii for a
constant 50 - n resistance.
table ii

1. block a on a horizontal friction - free table is accelerated by a force from

a string attached to block b. b falls vertically and drags a horizontally.
both blocks have the same mass m. (neglect the strings mass.)
circle the correct answers.
a. the mass of the system (a + b) is (m) (2m).
b. the force that accelerates (a + b) is the weight of (a) (b) (a + b).
c. the weight of b is (mg/2) (mg) (2mg).
d. acceleration of (a + b) is (less than g) (g) (more than g).
if b were allowed to fall by itself, not dragging a,
then wouldnt its acceleration be g?
yes, because the force that accelerates
it would only be acting on its own
mass - not twice the mass!
to better understand this,
consider 3 and 4 on the
other side!

Explanation:

Step1: Calculate acceleration for Table I (using \(F = ma\), \(a=\frac{F}{m}\))

For \(F = 100N\), \(m = 25kg\), \(a=\frac{100}{25}=4m/s^{2}\)
For \(F = 200N\), \(m = 25kg\), \(a=\frac{200}{25}=8m/s^{2}\)
For \(a = 10m/s^{2}\), \(m = 25kg\), \(F=ma = 25\times10 = 250N\)

Step2: Calculate acceleration for Table II (using \(F_{net}=F - F_{res}\), \(a=\frac{F_{net}}{m}\))

For \(F = 50N\), \(F_{res}=50N\), \(F_{net}=50 - 50=0N\), \(a = 0m/s^{2}\) (already given)
For \(F = 100N\), \(F_{res}=50N\), \(F_{net}=100 - 50 = 50N\), \(a=\frac{50}{25}=2m/s^{2}\)
For \(F = 200N\), \(F_{res}=50N\), \(F_{net}=200 - 50=150N\), \(a=\frac{150}{25}=6m/s^{2}\)

Step3: Answer sub - questions for Block A and B

a. The mass of system \((A + B)\) is \(m + m=2m\)
b. The force that accelerates \((A + B)\) is the weight of \(B\) (since \(B\) is the part of the system providing the driving force due to gravity)
c. Weight of \(B\) is \(W = mg\) (by formula \(W=mg\))
d. Using \(F = ma\), \(F = mg\) (weight of \(B\)), \(m_{total}=2m\), \(a=\frac{mg}{2m}=\frac{g}{2}\), so acceleration of \((A + B)\) is less than \(g\)

Answer:

Table I:

FORCE	ACCELERATION
\(200N\)	\(8m/s^{2}\)
\(250N\)	\(10m/s^{2}\)

Table II:

FORCE	ACCELERATION
\(100N\)	\(2m/s^{2}\)
\(200N\)	\(6m/s^{2}\)

a. \(2m\)
b. \(B\)
c. \(mg\)
d. less than \(g\)