Mathematics · Oct / Nov 2023 · Paper 51 · Question 3
YMA01
As printed in the paper
The question as text
3. A hammer is used to hit a tent peg into soft ground. The hammer has mass 1.8 kg and the tent peg has mass 0.2 kg. The hammer and tent peg are both modelled as particles and the impact is modelled as a direct collision. Immediately before the impact, the tent peg is stationary and the hammer is moving vertically downwards with speed 10 m s –1 Immediately after the impact, the hammer and tent peg move together, vertically downwards, with the same speed v m s –1
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
3(a)[2]
×
=
+
v = 9 (positive)
3(b)[3]
For tent peg,
0.2(
0)
I
= ±
v
−
or
For hammer,
1.8(
10)
−= ±
I
v
−
1.8Ns OR 1.8 kgms1 units needed.
3(c)[5]
0
=
9
2
+
2 (0.12)
a
OR
0
=
9
2
−
2 (0.12)
a
2
−
=
2
−
2
=
2
g
R
a
R
g
a
R =
690 or 695
N.B. Using u =10 for 9 can score M0A0M1A1A0 max
Using s = 12, can score M1A0M1A1A0 max
(9
+
0)
ALT 1
0.12
=
t
2
(
R
−
2 )
g t
= ×
2 9
R =
690 or 695
1
ALT 2
0.12
=
××
2 9
2
+
2
×
0.12
R
g
2
R =
690 or 695
Notes for question 3
(a)
M1
Forms CLM equation, condone sign errors and extra g’s and
any correct cancellation
cao
A1
(b)
Impulsemomentum equation, dimensionally correct, correct
M1
no. of terms. Condone sign errors.
N.B. M0 if g is included.
A1 correct unsimplified equation
A1
A1 cao must include units.
A1
(c)
Equation formed to find the acceleration. Must be
M1
dimensionally correct and have the correct no. of terms.
A1
Correct unsimplified equation. Note
a = −
337.5
M1
Use of F=ma. Must be dimensionally correct and have the
correct no. of terms.
A1
Correct equation, a does not need to be substituted but should
be consistent with their a from first equation.
N.B. Use the equation for a to define the positive direction.
A1
cao
ALT 1
M1
Equation(s) formed to find the time
A1
Correct unsimplified equation. Note
t =
2
=
0.02666..
75
Use of impmom equation. Must be dimensionally correct and
M1
have the correct no. of terms.
A1
Correct equation, t does not need to be substituted but should
be consistent with their t from first equation.
cao
A1
ALT 2
M2
Use of workenergy equation. Must be dimensionally correct
and have the correct no. of terms.
Correct unsimplified equation, 1 each error.
A2
A1
cao
(5
−
8 )
+
5(
−
λ
+
2
λ
j (m s1) isw
)
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